Denoising by Intrinsic Tensor Sparsity Regularization ” : Supplementary Material
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چکیده
In this supplementary material, we provide the proofs to Theorems 1 and 2 presented in the maintext. We also present more clarifications on the parameter settings in our experiment. Furthermore, we show more experimental results to further substantiate the effectiveness of our method. 1. Proofs to Theorems 1 and 2 We first give the following Lemma [4]. Lemma 1. (von Neumann’s trace inequality) For any m × n matrices A and B, with σ(A) = [σ1(A), σ2(A), ...σr(A)] T and σ(B) = [σ1(B), σ2(B), ...σr(B)] T , where r = min(m,n), being the singular values of A and B, Then tr(AB) ≤ σ(A)σ(B). The equality is achieved when there exists unitarians U and V that A = UΣAV T and B = UΣBV T are SVDs of A and B, respectively. Based on the result of Lemma 1, we can deduce the following theorem. Theorem 1. ∀ A ∈ Rm×n, the following problem:
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تاریخ انتشار 2016